Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Mihailescu, Eugen 2012. On some coding and mixing properties for a class of chaotic systems. Monatshefte für Mathematik, Vol. 167, Issue. 2, p. 241.

    HAMDAN, D. PARRY, W. and THOUVENOT, J.-P. 2008. Shannon entropy for stationary processes and dynamical systems. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 02,

    POLLICOTT, M. SHARP, R. TUNCEL, S. and WALTERS, P. 2008. The mathematical research of William Parry FRS. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 02,

    Vershik, A. M. and Gorbulsky, A. D. 2008. Scaled Entropy of Filtrations of $\sigma$-Fields. Theory of Probability & Its Applications, Vol. 52, Issue. 3, p. 493.

    Вершик, Анатолий Моисеевич Vershik, Anatolii Moiseevich Горбульский, Александр Давидович and Gorbulsky, Alexander Davidovich 2007. Масштабированная энтропия фильтраций $\sigma$-алгебр. Теория вероятностей и ее применения, Vol. 52, Issue. 3, p. 446.


Automorphisms of the Bernoulli endomorphism and a class of skew-products

  • William Parry (a1)
  • DOI:
  • Published online: 01 September 2008

We consider a class of skew-products with base the one-sided two-shift equipped with the (½, ½)Bernoulli measure and fibre either or the circle. We give conditions for the first kind to be isomorphic to the base itself and use this result to establish an isomorphism with the base for the second kind when a certain irrationalis very well approximated by rationals. A consequence is that there is a circle action of automorphisms commuting with theone-sided two-shift.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]R. L. Adler , L. W. Goodwyn and B. Weiss . Equivalence of topological Markov shifts. Israel J. Math. 27 (1977), 4963.

[4]G. A. Hedlund . Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3 (1969), 320375.

[6]S. Siboni . Ergodic properties of a class of skew-systems obtained by coupling the translations of the 1-torus with the endomorphism 2x mod 1. Nonlinearity 7 (1994), 11331141.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *